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Mathematics, 21.06.2019 23:30
Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.
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Mathematics, 22.06.2019 01:30
Norder to get a certain shade of blue paint, a mixer must have 5 parts white paint to 3 parts blue. if 4 gallons of paint must be mixed, how many gallons of white paint must be used?
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Mathematics, 22.06.2019 04:00
The roof of a farm silo is the shape of a hemisphere and is made of sheet tin. if the diameter of the silo is 126.5 feet, how much sheet tin is needed to make the roof? (use π = 3.1416.)
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